Given a population mean of 53.7 with a standard deviation of 1.3 and a sample size of 6, answer these questions:

Part A: What is the standard deviation of the sampling distribution of x?? Show your work.

Part B: What does the sample size need to be if you want the standard deviation of the sampling distribution of x? to be 0.325? Show your work. 

Answer:

A) 0.53

B) 16

population mean of 53.7 with a standard deviation of 1.3 and a sample size of 6

Part A: What is the standard deviation of the sampling distribution of x?? Show your work. (5 points)

The Standard deviation of the sampling distribution is the population standard deviation divided by the square root of the mean, shown in the following:

1.3/sqrt(6) = 0.53

Part B: What does the sample size need to be if you want the standard deviation of the sampling distribution of x? to be 0.325? Show your work. (5 points)

Plug 0.325 into the equation used above.

0.325 = 1.3/sqrt(n)

Reorganize and solve for n.

sqrt(n) = 1.3/0.325

sqrt(n) = 4

n = 16